Solution 10 to problem l21o35
Expressions |
Parameters |
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Back to problem l21o35
Expressions
The solution is given through the following expressions:
b40=0
5 2
----*a6 *b23
18
b39=--------------
2
a8
b38=0
10
----*a10*a6*b23
9
b37=-----------------
2
a8
b36=0
b35=0
b34=0
5
---*a6*b23
3
b33=------------
a8
5
---*a6*b23
3
b32=------------
a8
5
---*a6*b23
3
b31=------------
a8
5
---*a6*b23
6
b30=------------
a8
10 2
----*a10 *b23
9
b29=---------------
2
a8
b28=0
5
---*a10*b23
3
b27=-------------
a8
5
---*a10*b23
3
b26=-------------
a8
5
---*a10*b23
3
b25=-------------
a8
b24=0
5 3
---*a6 *b23
9
b22=-------------
2
a10*a8
20 2
----*a6 *b23
9
b21=--------------
2
a8
5 2
---*a6 *b23
6
b20=-------------
2
a8
10 2
----*a6 *b23
3
b19=--------------
a10*a8
5 2
---*a6 *b23
6
b18=-------------
a10*a8
2
5*a6 *b23
b17=-----------
a10*a8
2
5*a6 *b23
b16=-----------
a10*a8
20
----*a10*a6*b23
9
b15=-----------------
2
a8
10
----*a10*a6*b23
3
b14=-----------------
2
a8
5
---*a6*b23
3
b13=------------
a8
10*a6*b23
b12=-----------
a8
5*a6*b23
b11=----------
a8
20
----*a6*b23
3
b10=-------------
a8
5*a6*b23
b9=----------
a8
5
---*a6*b23
3
b8=------------
a8
b7=0
5*a6*b23
b6=----------
a10
10*a6*b23
b5=-----------
a10
10 2
----*a10 *b23
3
b4=---------------
2
a8
20
----*a10*b23
3
b3=--------------
a8
10
----*a10*b23
3
b2=--------------
a8
b1=b23
a12=0
1
a11=---*a6
2
a9=0
1 2
---*a6
2
a7=---------
a10
a6=a6
a5=a6
a4=0
3*a6*a8
a3=---------
a10
a2=2*a10
a1=a8
Parameters
Apart from the condition that they must not vanish to give
a non-trivial solution and a non-singular solution with
non-vanishing denominators, the following parameters are free:
b23,a6,a10,a8
Relevance for the application:
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2
df(u,t)=(u *a10*a8 + u *f(v,v)*a10*a6 + 2*u *a10 *u + 3*f(v ,v )*a6*a8
3x x x x 2x
1 2
+ ---*f(v,v )*f(v,v)*a6 + f(v,v )*a10*a6*u)/a10
2 x x
1
df(v,t)=v *a8 + ---*v *f(v,v)*a6 + v *a10*u
3x 2 x x
2 5 10 2
df(u,s)=(u *a10*a8 *b23 + ---*u *f(v,v)*a10*a6*a8*b23 + ----*u *a10 *a8*b23*u
5x 3 3x 3 3x
20 2
+ ----*u *u *a10 *a8*b23 + 5*u *f(v,v )*a10*a6*a8*b23
3 2x x 2x x
20
+ ----*u *f(v ,v )*a10*a6*a8*b23 + 5*u *f(v,v )*a10*a6*a8*b23
3 x x x x 2x
5 2 2 10 2
+ ---*u *f(v,v) *a10*a6 *b23 + ----*u *f(v,v)*a10 *a6*b23*u
6 x 3 x
10 3 2 2
+ ----*u *a10 *b23*u + 10*f(v ,v )*a6*a8 *b23
3 x 2x 3x
2 2
+ 5*f(v ,v )*a6*a8 *b23 + 5*f(v ,v )*f(v,v)*a6 *a8*b23
x 4x x 2x
2
+ 10*f(v ,v )*a10*a6*a8*b23*u + 5*f(v ,v )*f(v,v )*a6 *a8*b23
x 2x x x x
5 2 5
+ ---*f(v,v )*f(v,v)*a6 *a8*b23 + ---*f(v,v )*a10*a6*a8*b23*u
6 3x 3 3x
10 2 5 2 3
+ ----*f(v,v )*f(v,v )*a6 *a8*b23 + ---*f(v,v )*f(v,v) *a6 *b23
3 2x x 9 x
20 2 20 2 2
+ ----*f(v,v )*f(v,v)*a10*a6 *b23*u + ----*f(v,v )*a10 *a6*b23*u )/(
9 x 9 x
2
a10*a8 )
5 5 2
df(v,s)=(---*u *v *a10*a8*b23 + ---*u *v *a10*a8*b23 + v *a8 *b23
3 2x x 3 x 2x 5x
5 5
+ ---*v *f(v,v)*a6*a8*b23 + ---*v *a10*a8*b23*u
6 3x 3 3x
5 5
+ ---*v *f(v,v )*a6*a8*b23 + ---*v *f(v ,v )*a6*a8*b23
3 2x x 3 x x x
5 5 2 2
+ ---*v *f(v,v )*a6*a8*b23 + ----*v *f(v,v) *a6 *b23
3 x 2x 18 x
10 10 2 2 2
+ ----*v *f(v,v)*a10*a6*b23*u + ----*v *a10 *b23*u )/a8
9 x 9 x